Single-stage liquid-ring vacuum pump having double axial inlet

ABSTRACT

A single-stage liquid-ring vacuum pump having a double axial inlet with flat-distribution plates comprises a central body ( 2 ), an impeller ( 5 ) eccentrically housed in a chamber ( 4 ) delimited by the central body ( 2 ), a flanged suction manifold ( 15 ) in fluid communication with two suction openings ( 8 ) located at opposite ends of the central body ( 2 ), a flanged exhaust manifold ( 17 ) in fluid communication with two exhaust openings ( 9 ) located at opposite ends of the central body ( 2 ). The flanged suction manifold ( 15 ), flanged exhaust manifold ( 17 ) and feed manifold are integrated into the central body ( 2 ), so as to reduce weights and bulkiness as compared with the pumps of the known art, the pump performance being the same.

FIELD AND BACKGROUND OF THE INVENTION

The present invention relates to a single-stage liquid-ring vacuum pumphaving a double axial inlet with flat-distribution plates.

The present invention is particularly adapted for use in suction ofaeriform substances also containing small solid particles or wetaeriform substances that, by effect of the compression followingsuction, cause water condensation, which is noxious to other types ofpumps.

Pumps of this type are used in processes involving de-aeration,impregnation, boiling, vacuum condensation, distillation, drying,sterilization, filtration and solvent recovery.

By way of example, these pumps are therefore used in the sectorconcerning processing of plastic materials for example, where removal ofthe humidity that otherwise would be dangerous is required, or in allsectors in which it is necessary to create the vacuum, such as thepharmaceutical, chemical, petrochemical sectors, chemical or fooddistilleries, refineries, oil mills, dairies, etc.

Single-stage liquid-ring vacuum pumps having a double axial inletgenerally comprise a central body defined in the specific technicalfield as spacer. The spacer internally confines a cylindrical chamberhaving a regular or irregular circular section with a longitudinalextension axis that, when the pump is installed, is oriented in ahorizontal direction. Housed in the chamber is an impeller fitted on ashaft extending parallel to the longitudinal extension axis of thechamber and spaced apart therefrom. The impeller is therefore mountedeccentrically in the chamber. Installed on each of the opposite axialends of the spacer is a cover closing the chamber and having passagesfor admission and exhaust of the fluid to be pumped and of a workingliquid. In particular, each of the two covers internally has a firstcompartment open towards a first region of the chamber through a suctionopening formed in a head wall delimiting the chamber. The firstcompartment also communicates with a suction manifold through a flangedbody mounted on the cover itself. A second compartment opens on a secondregion of the chamber through an exhaust or pressurized opening formedin a head wall delimiting the chamber, which exhaust opening preferablyhas smaller sizes than the feeding opening. The second compartmentfurther communicates with an exhaust manifold through a flanged exhaustor pressurized body, mounted on the cover too. The flanged suctionbodies of the two covers are mutually connected by said suction manifoldwhich is defined by a pipe disposed above the spacer and preferablyrunning parallel to the longitudinal axis of the chamber. At anintermediate portion of the suction manifold there is a suction inletdesigned to be connected to the environment from which the fluid is tobe sucked.

The flanged exhaust bodies of the two covers are mutually connected bysaid exhaust manifold which is defined by a pipe disposed above thespacer and preferably running parallel to the longitudinal axis of thechamber. At an intermediate portion of the exhaust manifold there is anexhaust or pressurized outlet designed to be connected to theenvironment into which the sucked fluid is to be introduced.

Each of the two covers is further provided with a third compartment thatis open towards the chamber and communicates with a filling inlet forthe working liquid which is formed in a head wall delimiting thechamber. The feeding inlet is defined by an attachment element mountedon the cover itself and designed to be coupled, through suitable pipes,with a feeding source for supply of said working liquid.

In particular the working-liquid feeding system contemplates use of pipefittings and connecting pipes between each of the individual feed inletspresent on the covers and the main element for attachment to the plantwith, as a result, further complexity for installation of the pumpbefore use.

The impeller while being only one, is divided into two axial portionsworking in parallel.

The fluid sucked by the suction inlet is shared between the two flangedsuction bodies and enters the cylindrical chamber through each of thesuction openings present on the covers. At each of the two axialportions of the impeller, the fluid is enclosed between two successivevanes and a ring defined by the working liquid that, by effect of thecentrifugal force, lies close to the cylindrical side wall of saidchamber. The progressive volume variation created between the two vanesand the liquid ring, by virtue of the eccentric rotation of the impellerrelative to the spacer and the liquid ring, first creates a fluidexpansion and, subsequently, a fluid compression until said fluid isejected through the exhaust openings. The ejected fluid is then conveyedthrough the manifold into the single exhaust outlet.

However, the single-stage liquid-ring pumps having a double axial inletwith flat-distribution plates of known type which have been brieflydescribed above have many limits and drawbacks.

In particular, the Applicant has perceived that the bulkiness and weightof the pumps of known type should be reduced. In fact, the verticalbulkiness of known pumps is greatly affected by the presence of thesuction and exhaust manifolds that must be mounted on the pump itself.

Furthermore, also the presence of four flanges that are required forconnection of the two manifolds to the pump adversely affects thebulkiness and weight of the covers, and therefore the bulkiness andoverall weight of the pump itself because the flanged feeding inlets andexhaust outlets are positioned on the covers, and the flange size isfixed and strictly linked to the flow rate of the fluid to be treated.Under this situation, the technical task underlying the presentinvention consists in conceiving a single-stage liquid-ring vacuum pumphaving a double axial inlet with flat-distribution plates that iscapable of substantially obviating the mentioned drawbacks.

SUMMARY OF THE INVENTION

In particular, it is an aim of the present invention to propose asingle-stage liquid-ring vacuum pump having a double axial inlet withflat-distribution plates that is able to reduce the overall bulkinessand the pump weight and to optimize the suction and exhaust fluidmechanics, the provided performance being the same.

Within the scope of this technical task, it is an important aim of theinvention to conceive a single-stage liquid-ring vacuum pump having adouble axial inlet with flat-distribution plates that can be more easilytransported and installed.

The technical task mentioned and the aims specified are substantiallyachieved by a single-stage liquid-ring vacuum pump having a double axialinlet with flat-distribution plates that is characterized in that itcomprises one or more of the technical solutions claimed in the appendedclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

The description of a preferred but not exclusive embodiment of asingle-stage liquid-ring vacuum pump having a double axial inlet withflat-distribution plates in accordance with the invention is now givenby way of non-limiting example and illustrated in the accompanyingdrawings, in which:

FIG. 1 is an overall perspective view of a single-stage liquid-ringvacuum pump having a double axial inlet with flat-distribution plates inaccordance with the invention;

FIG. 2 shows an exploded view of the pump seen in FIG. 1;

FIG. 3 is a front view of the pump in FIG. 1;

FIG. 4 is a section view taken along line IV-IV in FIG. 3;

FIG. 5 is a section view taken along line V-V in FIG. 4;

FIG. 6 is a perspective view of a first element of the pump shown inFIG. 1;

FIG. 7 is a perspective view of a second element of the pump seen inFIG. 1; and

FIG. 8 is a front view of a third element of the pump seen in FIG. 1.

DESCRIPTION OF THE PREFERRED EMBODIMENT

With reference to the drawings, a single-stage liquid-ring vacuum pumphaving a double axial inlet with flat-distribution plates has beengenerally identified with reference numeral 1.

The pump comprises a central body 2 or spacer, better shown in FIGS. 2and 6. The central body 2 has a cylindrical side wall 3 of circular orsubstantially circular section, internally delimiting a cylindrical orsubstantially cylindrical chamber 4 having a longitudinal extension axis“X”.

Housed in chamber 4 is an impeller 5 fitted on a shaft 6, said shaftextending parallel to the longitudinal extension axis “X” of thechamber. The longitudinal axis “Y” of the shaft 6 is spaced from thelongitudinal extension axis “X” of the chamber (FIG. 4). In knownmanner, the impeller 5 is therefore eccentrically mounted in chamber 6,as better shown in FIG. 5. One end 6 a of the shaft 6 emerges from thepump to enable connection to a motor, not shown.

Formed at each of the two opposite axial ends 7 of the central body 2,i.e. on opposite faces of the cylinder defined by the body 2 itself, isa suction opening 8 and an exhaust opening 9 (FIG. 2).

The central body 2 further has an opening 10 (only visible in FIG. 7) ateach of said two axial ends 7, said opening being designed to feed aworking liquid 11 that will define the liquid ring.

In the preferred embodiment herein shown, these openings 8, 9, 10 areformed in a plate 12. As shown in FIGS. 2 and 4, each of the two plates12 closes a respective end 7 of the central body 2 and confines chamber4. In addition, each plate 12 lies close to an edge of the impellervanes 13 and to an end surface of the impeller hub 5 a, so that a workvolume for a fluid 14 to be treated is defined between two consecutivevanes 13 and together with the liquid ring.

Further auxiliary exhaust openings 9 a known by themselves and thereforenot further described can be present next to the exhaust opening 9, saidexhaust opening 9 having smaller sizes than the suction opening 8, asvisible in FIGS. 2 and 4. The auxiliary exhaust openings 9 a arepreferably closed by flexible blades or similar elements not shown thatunder the action exerted by the fluid, open when the pressure overcomesa predetermined threshold.

Both suction openings 8 are in fluid communication with a suctionmanifold 15 having a suction inlet 16 adapted to be connected to theenvironment from which the fluid 14 is to be sucked.

Both exhaust openings 9 are in fluid communication with an exhaustmanifold 17 having an exhaust outlet 18 adapted to be connected to theenvironment into which the previously sucked fluid 14 is to beintroduced.

The opening 10 designed to feed the working liquid 11 is in fluidcommunication with a feed manifold 19 having a feeding inlet 20 adaptedto be connected to a feeding source not shown, for supply of said liquid11.

Advantageously the suction manifold 15 and exhaust manifold 17 areintegrated into the central body 2. Preferably, the feed manifold 19 toois integrated into the central body 2.

In more detail, as better shown in FIGS. 2, 5 and 6, the suctionmanifold 15 and exhaust manifold 17 are formed close to the cylindricalside wall 3 of the central body 2 and are preferably located close to anupper portion of the pump 1, considering the installed pump 1 resting onthe ground with its longitudinal axis “X” disposed horizontally.

The two manifolds 15, 17 preferably extend parallel to the longitudinalaxis “X” and preferably are symmetric relative to a vertical planepassing through said longitudinal axis “X”.

In the preferred embodiment herein illustrated, the suction manifold 15and exhaust manifold 17 are formed of one piece construction, by meltingfor example, with the central body 2. The manifolds are formed in thethickness of the central body 2 wall.

The geometric configuration thus taken enables the suction and exhaustfluid mechanics to be optimized because generation of imbalances ordisequilibrium between the incoming and outgoing fluids is avoided.Therefore the construction symmetry outlined above gives furtheradvantageous aspects to the pump being the object of the invention.

Each of the two manifolds 15, 17 is confined by a convex portion 21 ofthe outer surface of the cylindrical wall 3 and by an arched portion 22having opposite edges oriented as generatrices of the cylindrical wall 3and joined to the cylindrical wall 3 itself (FIG. 6). The manifold shapeseen in cross section is not however given in a limiting sense. In factthe wall 22 can have different shapes and the outer surface of thecylindrical wall 3 can be such shaped as to give the manifold the mostappropriate section.

At an axially intermediate portion of the suction manifold 15, a suctionduct 23 of circular section is present and it preferably extendsvertically from said manifold 15 and terminates with the suction inlet16.

A flange 24 surrounds the suction inlet 16, is also preferably formed ofone piece construction with the suction duct 23 and the suction manifold15, and is used to connect the pump 1 to the environment from which thefluid 14 is to be drawn.

Likewise, at an axially intermediate portion of the exhaust manifold 17,an exhaust duct of circular section 25 is present which extendsvertically from said manifold 17 and terminates with the exhaust outlet18.

The flange 24 too surrounding the exhaust outlet 18 is preferably of onepiece construction with the exhaust duct 25 and the exhaust manifold 17and is used to connect the pump 1 to the environment into which thesucked fluid 14 is to be introduced.

As shown in FIGS. 2 and 6, also the feed manifold 19 for the workingliquid 11 is preferably integrated into the central body 2, in the samemanner as the manifolds 15, 17.

This feed manifold 19 is formed at the cylindrical side wall 3 of thecentral body 2 and is preferably located close to a lower side portionof pump 1.

In the preferred embodiment herein illustrated, the feed manifold 19extends parallel to the longitudinal axis “X” of the central body 2 andis of one piece construction, by melting for example, with the centralbody 2.

This feed manifold 19 is confined by a convex portion 26 of the outersurface of the cylindrical wall 3 and by an arched wall 27 havingopposite edges oriented as generatrices of the cylindrical wall 3 andjoined to the cylindrical wall 3 itself (FIG. 6).

An attachment element 28 is present at an axially intermediate portionof the feed manifold 19 and it extends from said manifold 15 andterminates with the feeding inlet 20 for supply of the working liquid11.

Said attachment element 28 too is preferably formed unitary, by meltingfor example, with the central body 2.

The wall 27 can have different shapes and the outer surface of thecylindrical wall 3 can be such shaped as to give the manifold the mostappropriate section.

To enable passage of fluid 14 from the suction manifold 15 to thesuction opening 8 and from the exhaust opening 9 to the exhaust manifold17, pump 1 comprises a pair of covers 29 each abutting against one ofthe ends 7 of the central body 2 (FIGS. 1 and 2).

Each cover 29 is mounted on one of the plates 12, said one platetherefore being interposed between the central body 2 and cover 29 (FIG.4); in this way the assembly tightness to the fluids is simplifiedbecause only a hermetic tightness between the cover 29 and plate 12 andbetween the plate 12 and central body 2 is required to be ensured. Inparticular the necessity of seals simultaneously operating on the threeparts is avoided, which would make the assembling process morecomplicated and would impair the overall pump reliability.

The two covers 29, two plates 12 and central body 2 are pack-wise closedby means of tie-rods 29 a passing through slots formed in the covers 29themselves (FIG. 1).

In addition, as better shown in FIGS. 2 and 7, each of the two plates 12has a first aperture 30 in register with the suction manifold 15 andshaped like the cross section of this manifold 15, a second aperture 31in register with the exhaust manifold 17 and shaped like the crosssection of this manifold 17 and a third aperture 32 in register with thefeed manifold 19 and shaped like the cross section of this manifold 19.The first, second and third apertures 30, 31, 32 are formed close to aperipheral edge of plate 12 (FIG. 7).

Cover 29 on a concave face 33 thereof facing the respective plate 12delimits a first compartment 34 (FIGS. 2 and 8) that, when pump 1 isassembled, is in fluid communication with the respective suction opening8 of plate 12 and with the suction manifold 15, a second compartment 35in fluid communication with the respective exhaust opening 9 of plate 12and with the exhaust manifold 17 and a third compartment 36 in fluidcommunication with the feed manifold 19 for the working liquid 11 andwith the respective opening 10 in plate 12 to supply said working liquid11.

Said compartments 34, 35, 36 are separated from each other by baffles 37and delimited by a peripheral edge 38 of cover 29 and an inner edge 39,said inner edge 39 surrounding a central hole 40 designed to receive theshaft 6 (FIGS. 8 and 4). Said shaft 6 further passes through a centralhole 40 a formed in each plate 12.

Each plate 12 has opposite flat surfaces, is coupled with one of theends 7 of the central body 2 on a single plane and is further coupledwith the respective cover 29 on a single plane. This flat couplingwithout coupling locators enables the working operations to besimplified, the production times and costs to be improved and thesealing capacity of the pump to be greatly increased.

In fact, the peripheral edge 38, inner edge 39 and baffles 37 of cover29 abut against plate 12 and are coplanar.

In addition, as shown in FIGS. 4 and 6, an end edge 41 of thecylindrical wall 3 and end edges 41 of the arched walls 22, 27 lie inthe same plane and abut against plate 12.

Each plate 12 has the respective suction opening 8 facing chamber 4 andthe first compartment 34, the respective exhaust opening 9 facingchamber 4 and the second compartment 35 and the respective opening 10for supply of the working liquid 11 facing chamber 4 and the thirdcompartment 36.

The first aperture 30 of plate 12 further faces the first compartment 34and the suction manifold 15, the second aperture 31 faces the secondcompartment 35 and the exhaust manifold 17 and the third aperture 32faces the third compartment 36 and the feed manifold 19.

Referring in particular to FIG. 4, a flange or box 42 carrying a bearing43 which supports shaft 6 is housed in each of the holes 40 of covers29.

Installed between each flange 42 and the shaft 6 is a rotating sealingelement 44 known by itself, which lies between the impeller 5 and therespective bearing 43. Possible liquid leakages are collected by meansof a pipe fitting 45 positioned in flange 42, said pipe fitting openinginto said flange 42 close to the shaft 6 between the sealing element 44and the respective bearing 43. Interposed between the bearing 43 andpipe fitting 45 is an annular gasket 46.

The collected liquid 11 can be recycled by connecting said pipe fittings45 to a circuit for re-introduction of the leaked liquid 11 into thefeed manifold 19.

Each of the two covers 29 has a pair of support feet 47 provided withholes for anchoring the pump 1 to a base.

Finally, as shown in the preferred embodiment in FIG. 4, the pump 1comprises an auxiliary flange, or bearing support, 48 located at the end42 a opposite to the end 6 a of the shaft 6 to be connected to the motorand housed in the main flange 42 in coaxial relationship.

The auxiliary flange 48 carries the bearing 43 supporting the shaft 6and is axially adjustable relative to the main flange 42, so as toeasily adjust the axial position of the shaft 6 and impeller 5 inchamber 4.

In particular, adjusting screws 49, not shown in detail, are used tomove the auxiliary flange 48 within the main flange 42 along an axialdirection, while locking screws 50 lock the two flanges 48, 42 to thedesired position, once adjustment has been carried out.

The pump in accordance with the invention achieves the intended purposesand offers many advantages.

In fact, the supplied performance being the same, the pump of theinvention is much more compact and lighter in weight than the pumps ofthe known art. The weight reduction as compared with pumps of sameperformance is about 30% and the reduction in volume is about 40%.

This result has been achieved because said suction and exhaust manifoldswith flanged inlets and outlets are integrated into the central body anda single-attachment feed is provided; in addition, due to the presenceof said single-attachment feed, the flanges for coupling to themanifolds and the feeding inlet present in covers of known pumps havebeen eliminated. Consequently, the two covers have been greatly reducedin size and bulkiness which has brought about an important reduction inweights and materials.

Furthermore, due to the reduced weight and bulkiness, the pump of theinvention can be transported and installed in a simpler and quickermanner.

Installation is also simplified as a result of the fact that theintegrated manifolds are already in place and must not be mounted insitu.

In addition, a feeding integrated with a single attachment element doesnot require pipe fittings and particular plant connections.

The compactness in an axial direction of the pump of the invention alsoenables the shaft length of the impeller to be reduced, as compared withknown pumps of same performance. This reduction, in addition toinvolving a decrease in the shaft weight, also gives rise to a reductionin the shaft bending during rotation and, therefore, to an importantvibration reduction.

The vibration reduction brings about, as a consequence, an increase inthe fatigue life of the pump components and a decreased operationalnoise.

1. A single-stage liquid-ring vacuum pump having a double axial inletcomprising: a central body (2) being formed with a suction opening (8)and an exhaust opening (9) at each of the central body two axial ends(7); an impeller (5) eccentrically housed in a chamber (4) delimited bysaid central body (2); a suction manifold (15) in fluid communicationwith both the suction openings (8) and having a suction inlet (16)adapted to be connected to an environment from which a fluid (14) is tobe sucked; an exhaust manifold (17) in fluid communication with both theexhaust openings (9) and having an exhaust outlet (18) adapted to beconnected to an environment into which the sucked fluid (14) is to bedischarged; the central body (2) being further provided, at each of saidtwo axial ends (7), with an opening (10) designed to feed a workingliquid (11) that will define a liquid ring; wherein the flanged suctionmanifold (15) and flanged exhaust manifold (17) are integrated into thecentral body (2).
 2. A pump as claimed in claim 1, wherein the suctionmanifold (15) and exhaust manifold (17) are formed close to a side wall(3) of the central body (2).
 3. A pump as claimed in claim 1, whereinthe suction manifold (15) and exhaust manifold (17) are formed of onepiece construction with the central body (2).
 4. A pump as claimed inclaim 1, further comprising a feed manifold (19) for supply of theworking liquid (11), which manifold is in fluid communication with saidfeed openings (10) and has a feeding inlet (20) adapted to be connectedto a feeding source for said working liquid (11); said feed manifold(19) being integrated into the central body (2).
 5. A pump as claimed inclaim 4, wherein the feed manifold (19) is formed close to a side wall(3) of the central body (2).
 6. A pump as claimed in claim 4, whereinthe feed manifold (19) is formed of one piece construction with thecentral body (2).
 7. A pump as claimed in claim 4, further comprising apair of covers (29), each abutting against one end (7) of the centralbody (2) and defining a first compartment (34) in fluid communicationwith the respective suction opening (8) and the suction manifold (15), asecond compartment (35) in fluid communication with the respectiveexhaust opening (9) and the exhaust manifold (17) and a thirdcompartment (36) in fluid communication with the feed manifold (19) anda respective opening (10) for supply of said working liquid (11).
 8. Apump as claimed in claim 7, further comprising a pair of plates (12),each abutting against one of the ends (7) of the central body (2), beinginterposed between said central body (2) and the respective cover (29)and confining the first, second and third compartments (34, 35, 36)together with the respective cover (29).
 9. A pump as claimed in claim8, wherein each plate (12) has the respective suction opening (8) facingthe chamber (4) and the first compartment (34), the respective exhaustopening (9) facing the chamber (4) and the second compartment (35), andthe respective opening (10) for supply of the working liquid (11),facing the chamber (4) and the third compartment (36).
 10. A pump asclaimed in claim 8, wherein each plate (12) further has a first aperture(30) in register with the first compartment (34) and the suctionmanifold (15), a second aperture (31) in register with the secondcompartment (35) and the exhaust manifold (17) and a third aperture (32)in register with the third compartment (36) and the feed manifold (19).11. A pump as claimed in claim 8, wherein each plate (12) has oppositeflat surfaces.
 12. A pump as claimed in claim 8, wherein each plate (12)is coupled with one of the ends (7) of the central body (2) in a singleplane.
 13. A pump as claimed in claim 8, wherein each plate (12) iscoupled with the respective cover (29) in a single plane.
 14. A pump asclaimed in claim 1, further comprising a suction duct (23) extendingfrom the suction manifold (15) and terminating with the suction inlet(16); said suction duct (23) being formed of one piece construction withthe central body (2).
 15. A pump as claimed in claim 1, furthercomprising an exhaust duct (25) extending from the exhaust manifold (17)and terminating with the exhaust outlet (18); said exhaust duct (25)being formed of one piece construction with the central body (2).
 16. Apump as claimed in claim 4, further comprising a feed attachment element(28) extending from the feed manifold (19) for supply of the workingliquid (11) and terminating with the feeding inlet (20); said attachmentelement (28) being formed of one piece construction with the centralbody (2).
 17. A single-stage liquid-ring vacuum pump having a doubleaxial inlet comprising: a central body (2) being formed with a suctionopening (8) and an exhaust opening (9) at each of the central body twoaxial ends (7); an impeller (5) eccentrically housed in a chamber (4)delimited by said central body (2); a suction manifold (15) in fluidcommunication with both the suction openings (8) and having a suctioninlet (16) adapted to be connected to an environment from which a fluid(14) is to be sucked; an exhaust manifold (17) in fluid communicationwith both the exhaust openings (9) and having an exhaust outlet (18)adapted to be connected to an environment into which the sucked fluid(14) is to be discharged; the central body (2) being further provided,at each of said two axial ends (7), with an opening (10) designed tofeed a working liquid (11) that will define a liquid ring; wherein theflanged suction manifold (15) and flanged exhaust manifold (17) areintegrated into the central body (2), and wherein the pump furthercomprises a feed manifold (19) for supply of the working liquid (11),which manifold is in fluid communication with said feed openings (10)and has a feeding inlet (20) adapted to be connected to a feeding sourcefor said working liquid (11); said feed manifold (19) being integratedinto the central body (2).
 18. A pump as claimed in claim 17, whereinthe feed manifold (19) is formed of one piece construction with thecentral body (2).
 19. A pump as claimed in claim 17, further comprisinga pair of covers (29), each abutting against one end (7) of the centralbody (2) and defining a first compartment (34) in fluid communicationwith the respective suction opening (8) and the suction manifold (15), asecond compartment (35) in fluid communication with the respectiveexhaust opening (9) and the exhaust manifold (17) and a thirdcompartment (36) in fluid communication with the feed manifold (19) anda respective opening (10) for supply of said working liquid (11).